With July 1, 1994 as a deadline, the European Union deregulated the property liability markets to a great extent. This led to the abolishment of twelve regional monopolies in property liability insurance in Germany. In Switzerland as well efforts are being made to deregulate the existing 19 cantonal monopolies in fire insurance in an attempt to follow the EU lead. This paper examines the possible outcome of an abolishment of the cantonal monopolies on the Swiss property liability insurance market, taking an indirect approach. It is based on a comparison of premium payments in the German monopoly regions on the one hand, and premium payments of private insurers on the other. For the period 1980 to 1994, mark-up on damage payments proved to be lower by 21 percentage points in the monopoly regions. This result is in line with a corresponding analysis of the Swiss property liability insurance market covering the period from 1984 to 1994: the cantonal monopolies in Switzerland have a mark-up on damage payments that is 47 percentage points lower than the mark-up of their private counterparts. In conclusion, the comparison of monopolies and firms operating in a free market environment points to the fact that a deregulation of the Swiss monopolies in property liability insurance would very likely result in higher premiums.